# Are there any descent symmetry tables for character tables of linear structures?

I know about tables containing information about descending in symmetry, i.e. from larger point groups to their sub-groups.

We can see such tables in this answer, or in this PDF.

My question is - does any similar table exist even for $$C_{\infty v}$$ and $$D_{\infty h}$$ point groups?

• On page 80 (Chapter 3) of 'Molecular Symmetry and Group Theory' by R. Carter, publ Wiley there are tables for the partial descent from $C_{\infty V} \to C_{2V}$ and $D_{\infty h} \to D_{2h}$ and more importantly with an explanation of how to derive them. – porphyrin Nov 18 '18 at 10:28
• @porphyrin Thank you! Do you mean the 2009 edition? – Eenoku Nov 18 '18 at 10:58
• my edition is 1998 but it should be in newer editions – porphyrin Nov 18 '18 at 15:01

$$\begin{array}{c|c} \hline D_{\infty \mathrm h} & D_\mathrm{2h} \\ \hline \mathrm{\Sigma_g^+} & \mathrm{A_g} \\ \mathrm{\Sigma_g^-} & \mathrm{B_{1g}} \\ \mathrm{\Pi_g} & \mathrm{B_{2g} + B_{3g}} \\ \mathrm{\Delta_g} & \mathrm{A_{g} + B_{1g}} \\ \mathrm{\Sigma_u^+} & \mathrm{B_{1u}} \\ \mathrm{\Sigma_u^-} & \mathrm{A_u} \\ \mathrm{\Pi_u} & \mathrm{B_{2u} + B_{3u}} \\ \mathrm{\Delta_u} & \mathrm{A_{u} + B_{1u}} \\ \hline \end{array}$$
$$\begin{array}{c|c} \hline C_{\infty \mathrm v} & C_\mathrm{2v} \\ \hline \mathrm{A_1 = \Sigma^+} & \mathrm{A_1} \\ \mathrm{A_2 = \Sigma^-} & \mathrm{A_2} \\ \mathrm{E_1 = \Pi} & \mathrm{B_1 + B_2}\\ \mathrm{E_2 = \Delta} & \mathrm{A_1 + A_2} \\ \hline \end{array}$$